It is important to be marmite. You want people to deselect you as well as select you then you know that those who do connect resonate with your message. You are looking for quality connections not quantity of connections.
You only need 20 clients to have a phenomenal £500k per year coaching business.
You can always test to see if the generic message converts better but make sure you look at deeper funnel metrics. I.e. You don't want more connections but of a poorer quality so they lead to less assessment and sales strategy calls and ultimately clients.
Do not use your connection conversion as a security blanket. Your focus is to sign clients.